Question

use the fundamental identities to simplify the expression.
1/tan^2x+1

Answer 1

@mathavraj

Answer 2

\[\sin^2(x)+\cos^2(x)=1\] is the most fundamental one
can you see how to get a \(\tan^2(x)\) out of this?

Answer 3

sec^2x?

Answer 4

^close...if the question is \[\frac{1}{\tan^2 x + 1}\] \(\sec^2 x\) is just the \(\tan^2 x + 1\) part

Answer 5

hmm, which fundamental identity should i use then? O:

Answer 6

so it snot necessary to change it"?

Answer 7

what i meant was, start with
\[\sin^2(x)+\cos^2(x)=1\] and to get tangent out of it, recall that \(\tan(x)=\frac{\sin(x)}{\cos(x)}\)
so divide everything by \(\cos(x)\) to get the new identity
\[\tan^2(x)+1=\frac{1}{\cos^2(x)}\]

Answer 8

then you have the reciprocal of \(\frac{1}{\cos^2(x)}\) which is \(\cos^2(x)\) and your answer

Answer 9

in other words \[\tan^2 x + 1 = \sec^2 x\]
substitute that
\[\frac{1}{\tan^2 x + 1} \implies \frac{1}{\sec^2 x} \implies \frac{1}{\frac{1}{\cos^2 x}} \implies \cos^2 x\]
just depends on how you view life

Answer 10

thank you :)